Zimmerman's Algorithm

by S. Andrew Swann Неизвестный Автор

  -2-1012

  Mrs. Waxman marked off the whole numbers on the line and stated that the number line went off to infinity in both directions. That made perfect sense to Julia. She already understood enough about the integers, she had a clear image of the whole numbers marching off to infinity.

  Then Mrs. Waxman said that there were an infinity of fractions on the number line, as many fractions as there were whole numbers. She divided up the number line. Again Julia understood, while it took Mrs. Waxman a while to convince her classmates. Between any two whole numbers, there were as many fractions as there were whole numbers. While her teacher droned on, Julia had amused herself by mentally constructing a proof. It took her a moment, but she soon could line up every possible fraction with a sequence of whole numbers. She could picture an infinite matrix, numerators changing by rows, denominators by columns . . .

  Then, while Julia was thinking through her proof, Mrs. Waxman made her mistake. She said that, in fact, there were as many numbers between zero and one as there were whole numbers.

  Julia had to speak up at that. She said it didn't make sense, that Mrs. Waxman had to be wrong. Mrs. Waxman, at first, was relieved at the outburst. For once Julia had shown what Mrs. Waxman thought was a flash of mathematical ignorance. Her response to Julia's assertion was to reassure the entire class that the space between zero and one could be divided into an infinite number of points, as could any segment on the number line.

  Julia was frustrated with Mrs. Waxman's blindness. She said again that she was obviously wrong with what she was saying. Of course she could put an infinity of points on the line, that wasn't the problem.

  Mrs. Waxman was dumbfounded for a few long moments.

  Julia carefully started to explain that there had to be more points between zero and one than there were whole numbers. However you would try to count those points, there would be an infinity of numbers that would fall into each of the holes between the numbers you did manage to count.

  Mrs. Waxman asserted that an infinity was an infinity. Julia kept insisting she was wrong, in front of the whole class. Infuriated, Mrs. Waxman sent her to the principal, and the principal sent her home with a note to her parents telling them that Julia was disruptive in class and talked back to the teacher.

  Her father wouldn't hear any explanations from Julia. He just strapped her with his belt and sent her to her room for four days.

  During that exile, she read Men of Mathematics, a book by E.T. Bell. Near the end she discovered the chapter on George Cantor and his discovery of transfinite numbers. She discovered the symbol, " N."

  "It was like a sign," Julia had told her sister, "A revelation. Until then I had trusted other people, adults, to tell me what truth was. I didn't need faith in them anymore. I knew that there was another truth, eternal, unchanging, and immune from Mrs. Waxman's assertions."

  "But what about God?" Ruth had asked her.

  "God is there," Julia said. "He is in the equations. His truth is decipherable to anyone who can reason far enough. God is a Theorem. Someday He will be proved."

  The story fit seamlessly into what Gideon knew about Julia Zimmerman. It even explained the symbol she used, " N." Though the Baptist in him was having trouble with "God is a Theorem."

  "What did she mean by that?" Gideon asked her.

  Ruth set down her fork and asked, "What's the point of spirituality, Detective Malcolm?"

  The air in the restaurant was suddenly dark and very still. Gideon lowered his own fork and looked into

  Ruth's eyes. He felt a vague embarrassment at not being more religious himself. He'd been raised Baptist by his father, but he hadn't been to church in ages. Before he'd been shot, he hadn't talked to God in years. Here was someone who was raised in a spiritual vacuum, and who seemed to've put more thought into the subject during one conversation with her sister than he had for most of his life.

  "I guess the point of it is to give us a meaning, a direction in life. Some sense of right and wrong. . ."

  "A reassurance that there's something else," Ruth said. She knocked gently on the table. "Something beyond this somewhat disappointing world we find ourselves in. Something better, purer, more right, more real."

  Gideon nodded.

  "It seems to be human nature from ancient times to believe that this world is but a pale reflection of a perfect, incorruptible realm. Plato said it was all shadows on the wall of a cave. The Greek geometers believed that literally everything had emerged from the sequence of natural numbers."

  "So what does Julia believe?"

  "She believes that mathematics is the only way we can see clearly into that perfect, incorruptible realm. She believes that any truth that it uncovers is a window into the mind of God."

  Gideon felt unconvinced. "But we're talking about something invented by man. How can that bear any relation to God? Even in somebody's mind?"

  "It's self-reinforcing. You can see echoes of mathematical behavior in everything from a fall of a stone to a nautilus shell. Julia believed that everything discovered by mathematics had some reflection in the physical world."

  Gideon nodded. "Did this have any relationship with the work she did at MIT?"

  "We didn't talk much after she went off to college. Only a few times while she was at MIT."

  "Dr. Nolan—he worked with her in the lab—said she was beginning to act as if the programs they were creating were living creatures . . ."

  "Computers always fascinated her." Ruth looked up at Gideon and watched him carefully. "Why are you here? You're out of your jurisdiction, and you're asking me questions that can't have any bearing on what happened."

  "I don't know what has a bearing, and what doesn't. Would her fascination with computers lead to her wanting the use of a Daedalus?"

  "I thought they had one where she works—worked."

  Gideon leaned back and thought. Of course Julia would have access to the NSA's Daedalus. What would she be doing that needed it? And why would she leave when she already had access . . . ?

  "Julia went off on her own tangents a lot, didn't she?"

  "What do you mean?"

  "The stories I hear about her, writing her own notebooks during calculus class, writing magic squares on her test papers. It sounds as if she was the type of person who would do her own private research on the side."

  Ruth narrowed her eyes at him, as if he was unearthing something she hadn't thought about. "What do you mean? She never said anything like that to me."

  "Think for a moment. The Evolutionary Theorems Lab published a lot of material, a lot of people did their own research there. When she left, though, she wiped all the computers. It was as if she was hiding her work, but most of the work—up to the whole Riemann business—was already public. Why get into a possible legal struggle with the university?"

  "I always thought that she was trying to get back at MIT for shutting her lab down."

  "Does that seem like her to you?"

  "What do you mean?"

  "You know her better. All I know is what people have told me. But she doesn't seem like a particularly vengeful person."

  Ruth looked across the table at Gideon, shaking her head. "Losing the lab was a big blow to her."

  "But it was out of character, wasn't it? She's the type that would let a wrong slide by and be satisfied she was right—I mean, when Waxman reprimanded her, Julia looked up George Cantor and found out she was right all along."

  "Yes."

  "Did she ever show Waxman that book? Your father?"

  Ruth leaned back. "No, at least she never said she did. But she was just a kid then."

  "The child who'd grow into the kind of person to strike out at an employer out of spite would make every effort to prove Mrs. Waxman wrong, preferably in front of the whole class."

  "But she wiped the computers. Out of character or not."

  Gideon nodded. "When people do something out of character, nine times out of ten, they're hiding something."

  "
Like what?"

  "Like her own private research. If she was doing something on her own, she might not have wanted MIT to have it. If that's the case, I'd wonder if she continued that work with the government's equipment." "Like what?"

  "Something she needs a Daedalus for."

  2.05 Wed. Mar. 18

  WHEN they left the restaurant, it was close to two-thirty. Gideon walked with Ruth back toward her apartment. He felt as if he was closer to understanding Doctor Julia Zimmerman, if no closer to understanding what she was doing.

  He was thinking over what Ruth had said, about Julia's belief in her mathematics, when he noticed something across the street. A man in a heavy leather coat was pacing them. The man's hands were in his pockets, and he seemed to be conspicuously not looking at Gideon and Ruth as they walked down the street.

  Ruth was saying something, but Gideon wasn't paying attention to her. He was looking ahead of them. On the sidewalk, walking toward them, was a man in a jogging suit, wearing a windbreaker. His hands were in his pockets, too.

  Gideon took Ruth's arm and started slowing down.

  "Are you all right?" Ruth asked as Gideon began exaggerating his limp.

  "Follow my lead," Gideon whispered.

  They were limping past a small bookstore. The front window display was filled with the covers from a lot of underground magazines. Inside, Gideon could see ranks of bookshelves facing the doorway.

  The man in the jogging suit was about ten yards away. His right hand was coming out of his pocket. Across the street, the man with the leather coat had stopped and looked as if he was about to cross the street.

  A small bell rang as a man walked out of the bookstore. While the door stood open, Gideon half tackled Ruth into the store while he grabbed for his own gun. "Back in the store," Gideon said, 'Take cover."

  Ruth froze for a moment. The man behind the counter began to say something, "Hey—what?"

  Then there was a sound like a soft explosion—like a sledgehammer pounding loose sand. It was accompanied by the sound of breaking glass. A hole appeared in the glass of the closing front door.

  With that, Ruth scrambled for the back of the store to take cover somewhere behind the shelves. The guy behind the counter dropped, and Gideon hoped it wasn't because he was hit.

  Gideon saw the guy with the jogging suit through the front window. His hands were out of his pockets, and he carried a wicked looking automatic sporting a silencer. He was running for the door.

  Gideon leveled his revolver and fired. Unlike the silenced automatic, this sounded like a gunshot. The bullet punched a hole in the window just behind the jogger. The jogger dropped out of Gideon's line of sight. There were others moving on the other side of the bookshop door.

  They dropped as well, before he could get a good look at them.

  Gideon didn't wait for them to reappear. He backed up, past the lines of shelves, toward the rear of the store. He was hoping there was a back way out of this place.

  As he ducked around the last bookshelf, Ruth grabbed him. "What the hell's going on?" she demanded.

  "We have to get out of here," Gideon looked around the rear of the bookstore and saw what he was searching for. A large fire door stood at the end of the corridor formed by a tall bookshelf and the rear wall. It said, in bright red letters, "Emergency Exit Only."

  There was the sound of breaking glass by the front of the store. Gideon grabbed Ruth and pushed her toward the exit.

  "Who are these people?"

  "CIA, NSA, I don't know—just that they're trying to shoot us."

  Ruth slammed through the door first. As soon as the door opened, the room was filled with the sound of a fire alarm. She pushed through, Gideon following on her heels, backing toward the fire door, his gun pointing back into the store.

  He saw the gunman start to duck around the bookshelf and he put two shots near the corner.

  Fragments of wood and paper flew into the air, and the follower ducked back around the corner of the bookshelf.

  The fire exit led into a narrow alley that was only open at one end. "Run," he yelled at Ruth. They had to get to the end of the alley before these guys cut off their only escape route. Ruth didn't need the encouragement, she was already running for the street. Gideon started running after her, but he could feel his injured leg resist the movement. He was barely twenty yards away from the door, and Ruth was almost at the street.

  The fire door began moving, and Gideon fired another shot next to the open side of the door. The shot echoed in the alley, and orange sparks flew from the brick near the handle of the door. For the moment it stopped moving.

  Then he heard Ruth scream, "Shit!"

  Gideon turned to look toward the mouth of the alley. A black Lincoln Town Car had pulled up, passenger side facing the alley, blocking their escape. Ruth was only a few feet from it.

  The rear door opened and someone yelled from inside. "Quick, get in!"

  Whoever they were, they weren't trying to shoot them. Ruth didn't appear to debate the matter. She dove into the back seat, Gideon started running, his limp trying to slam him into the wall of the alley with every other step. As he closed on the car, the front passenger door opened, and a large man stepped out.

  He wore a charcoal-gray suit and a black tie, and in his hands he held a silenced Uzi.

  Gideon threw himself on the ground as the guy started firing. He was close enough to him that he could hear the hot brass casings bounce around and over him as the gunman emptied the Uzi's clip into the alley.

  "Come on, move it," the gunman called as Gideon heard him change clips.

  Gideon pushed himself up and scrambled for the back seat of the Lincoln, landing on his side next to Ruth, somehow keeping his grip on his gun. Outside the car, he heard the sound of the muffled Uzi reverberate through the car. He managed a look back down the alley and could see someone attempting to return fire, using the metal door for cover. The door itself was peppered with dozens of holes, and the men following them didn't dare give up their cover while the Uzi was firing.

  The man with the Uzi kicked the passenger door shut after Gideon was fully inside. He let a few more shots go into the alley, and then he slipped into the passenger seat. The Lincoln was accelerating away before he'd even closed the door.

  "Well," said the driver, sparing a glance back at Gideon and Ruth, "I guess we're in it now."

  "Who are you people?" Ruth asked.

  The man who'd carried the Uzi shook his head. "It would be inadvisable to tell you that. Suffice it to say that it's not in our best interests to allow you to fall into the hands of those people."

  "And who are they?" Ruth asked.

  Gideon sat up. There was something vaguely familiar about these guys.

  Now that he could see where the Lincoln was going, they were shooting north, weaving in and out of traffic. They blew through lights as yellow cabs blared horns at them.

  Gideon noticed a livid bruise on the neck of the man with the Uzi. "You were at my house," Gideon said.

  "You're worth keeping track of," said the driver. "We're not the only ones of that opinion."

  "What's going on?" Ruth yelled with frustration bordering on hysteria.

  "We'll explain what we can, when we can," the gunman told them as they tore through another intersection and made a screeching turn following signs toward the Holland Tunnel. While the one drove like a maniac, the other picked up a cellular phone and dialed someone. "Hi, Mom," the guy said. "Uncle had a bit of a breakdown. We had to pick him up. We got some groceries and we're heading to Abe's house. Yeah, I think you better call Triple-A." He hung up.

  "Uncle?" Gideon said.

  "We're going to take you to a safe house, check you both out for listening devices, then we'll see what we can talk about."

  The Lincoln slid into the tunnel. Gideon raised his gun and said, "I'd like an explanation now."

  "You better put that away," said the driver. "We don't want things to get ugly." The Lincoln started slowi
ng down. "I could let you both out here. But neither of us is going to discuss anything before we get where we're going." The car was almost stopped, and behind them horns were blaring at them. "Now either put that away, or get out."

  Gideon considered forcing the issue, but he didn't know if he wanted to. He would be putting Ruth in danger if he started pulling macho shit now. And whatever was going on, these guys seemed to be at least partially on his side.

  He holstered the gun.

  On the far side of the Hudson, they drove through Jersey City. They wove through so many twists and turns that Gideon was unsure exactly where they were when they entered a residential area and pulled into a weed-shot driveway. The house was in a run-down neighborhood, and looked as decrepit as the buildings to either side. The paint had once been red, but had faded to a chipped, weathered brown. Two windows were covered by sheets of plywood.

  The garage didn't look all that safe. The walls were tilted to the left, as if the whole thing was about to collapse. Despite that, the door slid up silently on its own as the Lincoln drove up the broken driveway. The car slid into the broken-down garage and the door started closing immediately. Gideon looked outside and saw that there seemed to be a few new timbers bracing the garage upright in its awkward position.

  The driver waited until the door was completely closed behind the Lincoln before he said, "Could we have the gun, please?"

  Gideon didn't like the way things were going, but he decided that there was little to gain by not playing along. Ruth was looking at him as if she blamed him for what was happening. For all he knew, she might be right. He handed the butt of the gun to the driver.

  The other man got out and opened the passenger door next to Gideon. "Come on," he said. As Gideon got out of the car, the man took a small wand from off of a shelf of old tools lining the wall of the garage. Unlike the rusty hacksaws and miscellaneous junk scattered on the shelf, this thing looked brand new. He flipped a switch on the thing and swept Gideon up and down as if it was a metal detector.